Final answer:
The moon phase after the full moon with a decreasing illuminated portion is known as the waning gibbous phase. This phase is visible for about a week after the full moon and precedes the third quarter phase, where half of the moon's surface is illuminated.
Step-by-step explanation:
The moon phase that follows the full moon when the sunlit portion visible from Earth starts to decrease is known as the waning gibbous phase. This is a period when more than half of the Moon's face appears illuminated, but less so each night. After the full moon peaks, its illumination diminishes, leading to what we refer to as the waning phases. About a week after the full moon, the Moon reaches the third quarter phase, during which we see exactly half of the Moon's illuminated side.
It's fascinating that the Moon appears lit in various ways at different times, which relates to its position in orbit around Earth and the angle at which sunlight strikes it. Observing the Moon's surface details is particularly intriguing during the first or third quarter phases, when shadows cast by topographical features provide the greatest relief and the most information about the Moon's surface.
In the cycle, after the full moon and before the third quarter, the decrease in the illuminated part of the Moon offers brilliant night skies, often aiding nighttime navigation for both romantics on strolls and students after late-night studies or social activities.